1. Field of the Invention
The present invention relates generally to complex bandpass analog-to-digital converters. More specifically, the present invention relates to techniques for providing complex bandpass modulator implementations for delta-sigma analog-to-digital converters.
2. Description of the Related Art
Many devices utilize analog-to-digital converters (ADCs) to convert analog information to digital information so that signal processing may be accomplished on the digital side. In particular, delta-sigma ADCs are useful in providing digital information that may be further processed by digital signal processing. Such delta-sigma ADCs convert incoming signals in a particular frequency span of interest into a high rate (oversampled), low resolution (often one-bit) digital output stream. The ratio of the output data rate to the frequency span of interest is known as the oversampling ratio. The delta-sigma approach to analog-to-digital conversion, with relatively high oversampling ratio, is well known for its superior linearity and anti-aliasing performance compared to traditional conversion approaches with low oversampling ratios.
This superior performance has led to the development and widespread use of practical delta-sigma ADCs in applications where the frequency span of interest is centered near or at DC. Such applications are commonly known as "lowpass" or "baseband" converters. It has been recognized that the superior performance of delta-sigma conversion in principle is not confined to lowpass conversion, but should also be possible to achieve for applications in which the frequency span of interest is centered around a frequency distant from DC. Such applications are known as "bandpass" converters, and they can play an important role in a wide variety of systems. In many radio systems for example, the signal of interest is centered around some intermediate frequency (IF) which is distant from DC, and a bandpass converter is desirable for conversion of the IF signal to digital format, whereupon digital signal processing techniques can be applied to yield important improvements in the overall radio system performance. A digital receiver within an AM/FM radio is one example of a device that can benefit from the use of such a bandpass ADC.
The desire to extend the advantages of the delta-sigma conversion approach into the bandpass realm is evident from efforts disclosed in Ribner et al. U.S. Pat. No. 5,283,578 issued Feb. 1, 1994, Jackson U.S. Pat. No. 5,442,353 issued Aug. 15, 1995, and Singor et al., "Switched-Capacitor Bandpass Delta-Sigma A/D Modulation at 10.7 MHz", IEEE Journal of Solid-State Circuits, vol. 30, No. 3, Mar. 1995, pp 184-192, all of which are herein incorporated by reference. All of these disclosed approaches, however, fail to achieve the degree of performance displayed by lowpass delta-sigma conversion, in part because they implement "real" bandpass converters, in which a single input signal is converted to a single stream of digital output values.
In order to maintain the full performance of lowpass delta-sigma conversion in a bandpass delta-sigma converter, it would be necessary to implement a "complex" bandpass converter, which can be thought of as converting a pair of input signals X and Y into two streams of digital output values, one such stream representing the "real" or "in-phase" (I) component of the signal, and the other such stream representing the "imaginary" or "quadrature" (Q) component of the signal. It is convenient and common to represent the two output data streams I and Q as a single complex data stream I+jQ, where j is a symbol representing the square-root of -1. Similarly, it is conventional to represent the two input signals as a single complex input X+jY. To understand why complex conversion would be necessary to realize the full benefits of bandpass delta-sigma conversion, it is important to understand some factors that can limit the performance of delta-sigma converters in general. A brief description of these factors is provided below.
The advantage of delta-sigma conversion comes at some expense, namely that the quantization of the signal to low resolution produces noise in the output data stream. The important job of the modulator is to "shape" this quantization noise out of the frequency range which contains the desired signal, so that subsequent digital filtering operations can recover the desired signal without corruption. For a given oversampling ratio, increasing the converter performance in terms of output signal-to-noise ratio (SNR) or dynamic range requires increasing the modulator performance or complexity (known as the modulator "order"). If the modulator performance is essentially optimal, the only choice is to increase the modulator order.
As the modulator order increases, however, it becomes increasingly difficult to keep the converter stable, and a point of diminishing returns is rapidly reached. Thus to get the highest SNR or dynamic range performance from a delta-sigma converter, it is advantageous to keep the modulator order as low as possible consistent with the noise shaping requirements. From this standpoint, a real bandpass modulator is at a severe disadvantage compared to a lowpass modulator because a real bandpass modulator requires double the order of a lowpass modulator to achieve a given noise shaping characteristic. By contrast, a complex bandpass modulator of given order N achieves the same noise shaping characteristic as a lowpass modulator of order N. Put another way, an optimal complex bandpass modulator of order N achieves performance equivalent to an optimal real bandpass modulator of order N operating at twice the oversampling ratio.
An example of the significant advantages of the complex bandpass approach relative to the real bandpass approach is discussed in Jantzi et al., "Quadrature Bandpass .DELTA..SIGMA. Modulation for Digital Radio", IEEE Journal of Solid-State Circuits, vol. 32, No. 12, Dec. 1997, pp. 1935-1950, incorporated herein by reference, which discloses a 4th-order complex bandpass delta-sigma converter with SNR 21 dB higher than a complex bandpass converter composed of two real 4th-order bandpass delta-sigma converters. Theoretical analysis of delta-sigma converters indicates that SNR should improve by 3+6N dB per doubling of the oversampling ratio, where N is the modulator order. According to the previous discussion, this indicates that a 4th-order complex bandpass delta-sigma converter should have 27 dB higher SNR than a 4th-order real bandpass converter. Furthermore, using two real bandpass converters to make a complex bandpass converter should result in an SNR for the complex converter which is 3 dB better than the SNR of the constituent real converters. This predicts that Jantzi et al. should have achieved a 24 dB improvement rather than the 21 dB observed if the configuration was optimal.
Looking at the structure disclosed by Jantzi et al., the sub-optimal performance arises from the fact that the modulator is not truly 4th-order complex. Rather, two of the orders are complex bandpass, and another two of the orders form a real bandpass element. A fully complex modulator is not practical for this structure because component mismatches, which are inevitable in any real implementation, cause a catastrophic degradation of SNR due to mixing of quantization noise from negative frequencies to positive, and vice-versa. Component mismatches in this structure also cause image-rejection degradation, which occurs when input signals outside the frequency range of interest are mixed into the desired signal frequency range by the mismatches. Both of these effects prevent the structure disclosed from achieving optimal bandpass delta-sigma converter performance. The disclosed structure is still superior to using two real bandpass converters, or to other approaches such as disclosed in Ong et al., "A Two-Path Bandpass DS Modulator for Digital IF Extraction at 20 MHz", IEEE Journal of Solid-State Circuits, vol. 32, No. 12, Dec. 1997, pp. 1920-1934, incorporated herein by reference, which do not have strong cross-coupling between the I and Q paths. However, it still fails to realize the fill performance potential of bandpass delta-sigma conversion, due to its sensitivity to mismatches.
The requirement for strong cross-coupling in order to achieve optimal bandpass delta-sigma converter performance is discussed in Jantzi et al. and also discussed in Stikvoort U.S. Pat. No. 5,764,171 issued Jun. 9, 1998, incorporated herein by reference. Stikvoort discloses a complex bandpass delta-sigma converter which uses cross-coupling between two continuous-time modulators to improve the noise-shaping performance without increasing the modulator order. Continuous-time modulators, however, suffer from performance degradation due to amplifier and comparator slewing effects. These slewing effects can generally be reduced in switched-capacitor (discrete-time) modulators by designing for adequate settling between samples.
The problem of removing the effects of mismatches in complex bandpass modulators, however, remains. Severe degradation of SNR and image rejection due to mismatches prevent prior bandpass modulators from achieving the performance benefits of fully complex bandpass modulators. In prior modulators, no method is known for removing the degradation effects of mismatch, other than to reduce the mismatch to sufficiently low levels. Beyond certain levels, however, such mismatch reduction becomes difficult and impractical.